Our subject experts have made RS Aggarwal Solutions for classes 6 to 12 available for free PDF download. It aids in the promotion of a thorough understanding of concepts in a very straightforward and precise manner. Our experts conduct extensive research before preparing the study materials. It also aims to provide simple and accurate answers to all of the problems in the RS Aggarwal textbooks. RS Aggarwal Maths Solutions can help develop rational thinking and a logical approach through in-depth explanations, practice questions, and solved examples. This aids in the promotion of conceptual clarity. Students will master the subject with the help of the solutions and achieve high grades by answering the questions asked in the examinations.
This is the most basic class, with the basic chapter forms the building blocks for more complex concepts taught in higher classes. Chapter 1 deals with the Number System. Number System covers topics such as the international system of representation of numbers, number comparisons, word problems involving number operations, estimation, etc. Finding prime and composite numbers from 1 to 100, divisibility tests, general properties of divisibility, prime factorisation, HCF and LCM and their properties are discussed in the second chapter. Concepts of chapter 3 are whole number operations, subtraction in whole numbers, multiplication of whole numbers, properties of multiplication and division of whole numbers. In the fourth chapter, we have integers on a number line and their operations and attributes. Operations on integers, properties of addition, subtraction, multiplication and division on integers.
Proper, improper, and mixed fractions, equivalent fractions, like and unlike fractions, comparison of fractions, the addition of fractions, subtraction of fractions, and objective problems are in the fifth chapter. Simplification is covered in Chapter 6. Here, the concepts of BODMAS learnt in previous classes to accomplish division, multiplication, addition, and subtraction operations on numbers and fractions. Like and unlike decimals, comparing decimals, converting a decimal into a fraction, turning a fraction into a decimal, operations of decimals are some of the main subjects covered in chapter 7. The usage of grouping symbols, operations on variables and integers, and algebraic expressions such as monomial and binomial operations on algebraic expressions are covered in the eighth chapter. Linear Expression is present in chapter 9. The concepts discussed are a linear equation by the trial-and-error method, systematic method for solving an equation, transposition and applications of equations.
Converting a given ratio to its simplest form, the ratio of two quantities in the same units, comparison of ratios, proportion, three numbers in proportion are covered in chapter 10. Concepts in chapter 11 are plane, point, line segment, ray, line, intersecting lines etc. Parallel lines, the distance between two parallel lines etc., are present in chapter 12. Interior and exterior of an angle, the magnitude of an angle and its measurement, units of measuring an angle, many types of angles, etc., are among the topics discussed in chapter 13. Drawing the perpendicular bisector of a given line segment, bisecting a given angle, drawing a line perpendicular to a given line from a point outside it, drawing a line parallel to a given line from a point outside it, and constructing some special angles using a pair of compasses are covered in the 14th chapter. Topics in the 15th chapter are straight line, curve, closed figures, open figures, sides, vertices and diagonals. Chapter 16 covers congruent triangles, the interior and exterior of a triangle, several triangles such as equilateral, isosceles etc., naming triangles based on their angles and the solutions provided by the Aakash solutions very accurate and helpful in understanding these topics.
Concepts related to quadrilaterals in chapter 17 are convex and concave quadrilaterals, interior and exterior of a quadrilateral, angle sum property of a quadrilateral, various types of quadrilaterals. The interior and exterior of a circle, the diameter of a circle, the chord of a circle, the secant of a circle, the circumference of a circle, segments of a circle, and other topics are covered in Chapter 18. The ideas of Three-Dimensional Shapes are covered in Chapter 19. Chapter 20 provides an in-depth study of Two-Dimensional Reflection Symmetry (Linear Symmetry). Chapter 21 deals with the Concept of Perimeter and Area. The perimeter of a rectangle, square, circumference of a circle, area of a square and rectangle are discussed here. Chapter 22 has topics like raw data, array, tabulation of data, observations, observation frequency, and statistics. Chapter 23 gives information about Pictograph. In the 24th chapter, students learn how to draw a bar graph. These chapters are very basic, yet the questions can be troublesome for the sixth-grader. The Aakash RS Aggarwal Solutions help with these questions.
Chapter 1 - Number System
Chapter 2 - Factors and Multiples
Chapter 3 - Whole Numbers
Chapter 4 - Integers
Chapter 5 - Fractions
Chapter 6 - Simplification
Chapter 7 - Decimals
Chapter 8 - Algebraic Expressions
Chapter 9 - Linear Equation in One Variable
Chapter 10 - Ratio, Proportion and Unitary Method
Chapter 11 - Line Segment, Ray and Line
Chapter 12 - Parallel Lines
Chapter 13 - Angles and Their Measurement
Chapter 14 - Constructions (Using Ruler and a Pair of Compasses)
Chapter 15 - Polygons
Chapter 16 - Triangles
Chapter 17 - Quadrilaterals
Chapter 18 - Circles
Chapter 19 - Three-Dimensional Shapes
Chapter 20 - Two-Dimensional Reflection Symmetry (Linear Symmetry)
Chapter 21 - Concept of Perimeter and Area
Chapter 22 - Data Handling
Chapter 23 - Pictograph
Chapter 24 - Bar Graph
In Chapter 1, we study addition, subtraction, multiplication and division of integers, and properties of addition, subtraction, multiplication, and division of integers. Chapter 2 deals with Fractions, addition and subtraction of fractions, multiplication and division of fractions, along with the method of changing unlike fractions to like fractions, comparing more than two fractions and reciprocal of the fraction. Methods of converting a decimal into a fraction, a fraction into a decimal, addition and subtraction of decimals, multiplication of decimal by 10,100, 100, etc., division of decimals by 10, 100, 1000, etc., are among the topics covered in Chapter 3. Chapter 4 - Rational Numbers deals with the concept of rational numbers, p/q form, positive rational numbers, negative rational numbers, etc. Chapter 5 includes exponents, laws of exponents, expressing large numbers in standard form, numbers in expanded form, square root. Chapter 6 covers the concepts of addition, subtraction and multiplication of algebraic expressions, multiplication of monomials and a binomial, multiplication of two binomials. Solving equations, transposition, and conversion of word problems into equations for obtaining the desired result are discussed in chapter 7. Chapter 8 deals with Ratio and Proportion, and its related topics are terms of ratio, comparison of ratios.
Chapter 9 discusses the topic Unitary Method, direct variation, inverse variation, and contains word problems. Topics covered in the 10th chapter are converting a fraction into a percentage, converting a percentage into a fraction, percentage as a ratio, converting a given ratio into a percentage, converting a given percentage in decimal form, etc. Topics such as profit and loss are discussed in chapter 11. Other topics discussed are gain percentage and loss percentage. Simple Interest is the centre of discussion in the 12th chapter. The phrases principle, Interest, amount, and rate are used and explained. In Chapter 13, Lines and Angles deals with supplementary angles, complementary angles, adjacent angles, linear pair angles, and vertically opposite angles. The Properties of Parallel Lines topic is discussed in Chapter 14 and the distance between parallel lines, transversal, and angles created when a transversal intersects two parallel lines.
Chapter 15 explores the properties of Triangles, naming triangles by considering the length of their sides, considering their angles, angle sum property of a triangle, exterior and interior opposite angles, etc. Chapter 16 discusses congruence, types of congruent figures, congruence of triangles, congruence and area. The SSS, SAS, ASA criteria for congruence are discussed in detail. Chapter 17 deals with the geometrical construction of various figures. Chapter 18 - Reflection and Rotational Symmetry covers reflection symmetry, rotational symmetry, and figures having line symmetry and rotational symmetry. Chapter 19 introduces Three-Dimensional Shapes and deals with solids, cuboid, cube, cylinders, cone and sphere. In Chapter 20, Mensuration, we shall view the problems related to a square, a rectangle, the areas of parallelograms, triangles and trapezia, etc. Chapter 21 discusses the topic of collection and organisation of Data. Topics covered in this chapter are mean of ungrouped data, mean of tabulated data, median of ungrouped data, median of discrete series, mode of ungrouped data.
In Chapter 22 - Bar Graphs, you will learn how to drawbar graphs step by step, reading bar graphs and types of bar graphs. Probability is the subject of Chapter 23. It is worked out by finding the ratio of the number of occurrences of the desired event by the number of occurrences plus the number of occurrence failures. There are many topics in this grade where the concepts introduced are new, whereas many topics have been improved upon from last year. Concepts like statistics and probability are crucial for higher grade mathematics, and to consolidate the concepts here, Aakash provides the RS Aggarwal Solutions.
Chapter 1 Integers
Chapter 2 Fractions
Chapter 3 Decimals
Chapter 4 Rational Number
Chapter 5 Exponents
Chapter 6 Algebraic Expressions
Chapter 7 Linear Equations in One Variable
Chapter 8 Ratio and Proportion
Chapter 9 Unitary Method
Chapter 10 Percentage
Chapter 11 Profit and Loss
Chapter 12 Simple Interest
Chapter 13 Lines and Angles
Chapter 14 Properties of Parallel Lines
Chapter 15 Properties of Triangles
Chapter 16 Congruence
Chapter 17 Constructions
Chapter 18 Reflection and Rotational Symmetry
Chapter 19 Three-Dimensional Shapes
Chapter 20 Mensuration
Chapter 21 Collection and Organisation of Data (Mean, Median and Mode)
Chapter 22 Bar Graphs
Chapter 23 Probability
The solutions provided by the Aakash Institute become all the more important because many concepts have been introduced, and this is the last step for the student to consolidate the mathematics concepts before stepping into the high school section. The standard form of a rational number, representation of rational numbers on the real line, addition of rational numbers, subtraction of rational numbers, multiplication of rational numbers, division of rational numbers are all covered in Chapter 1. Exponents of a rational number and related concepts such as rules of exponents, positive integral exponent of a rational number, and standard form of a number are covered in Chapter 2. The concept of squares, perfect squares, attributes of perfect squares, a product of two successive odd or even numbers, column and diagonal techniques for squaring a given number, the concept of square root, etc., are all covered in Chapter 3.
In Chapter 4, we shall see the cube of a number, its properties, shortcut method for finding the cube of a two-digit number, cube root of a positive perfect cube, etc. Chapter 5 presents numbers in a generalised form and numerous divisibility tests, and the replacement of alphabets with appropriate digits. Chapter 6 discusses Algebraic Expressions, addition, subtraction, multiplication and division of algebraic expressions. Chapter 7 includes topics that introduce factorisation when a common monomial factor occurs in each term by grouping. Chapter 8 has equations, their definitions, rules for solving a linear equation, transposing, etc. The 9th chapter is about percentage and problems based on it. Chapter 10 deals with profit and loss, advance concepts mentioned, i.e., discount, sales tax (ST), value-added tax (VAT).
In Chapter 11, compound interest and applications of compound Interest are introduced. We calculate compound Interest by using formulae. Chapter 12 deals with the topic of direct and inverse proportions. Chapter 13 contains topics like calculating work done by people. This is the application of the Unitary method taught in the previous classes. Chapter 14 contains simple open curves, polygons, types of polygons, properties of polygons like exterior angles, interior angles, the sum of those angles and the number of diagonals. Chapter 15 deals with the topic of Quadrilaterals, their vertices, sides, angles and diagonals of quadrilaterals. It also includes the "angle sum property of quadrilateral". Chapter 16 discusses the topic parallelogram, rhombus, rectangle, square, trapezium and their properties.
In Chapter 17, we construct types of quadrilaterals based on the requirements given. Chapter 18 deals with the topics like area of a trapezium, area of a polygon, area of a quadrilateral, irregular polygons and regular polygons. In the 19th chapter, students concentrate on faces, vertices and edges of a three-dimensional figure such as cuboid, cube, pyramid etc. Chapter 20 constitutes topics related to Volume and Surface Areas of Solids like cube, cuboid and right circular cylinder. Chapter 21 focuses on frequency distribution, data grouping using a distribution table, and histogram display. Chapter 22 introduces the plotting of the bar graphs and builds further into the interpretation of bar graphs. A line graph, double line graph, reading the given line graph, reading the double line graph are discussed in Chapter 23. Chapter 24 discusses constructing a pie chart for a given data using the formula to calculate the central angle. Chapter 25 builds upon the concepts of probability introduced in the previous class and contains some problems related to the topic.
Chapter 1 - Rational Numbers
Chapter 2 - Exponents
Chapter 3 - Squares and Square Roots
Chapter 4 - Cubes and Cube Roots
Chapter 5 - Playing With Numbers
Chapter 6 - Operations on Algebraic Expressions
Chapter 7 - Factorisation
Chapter 8 - Linear Equations
Chapter 9 - Percentage
Chapter 10 - Profit and Loss
Chapter 11 - Compound Interest
Chapter 12 - Direct and Inverse Proportions
Chapter 13 - Time and Work
Chapter 14 - Polygons
Chapter 15 - Quadrilaterals
Chapter 16 - Parallelograms
Chapter 17 - Construction of Quadrilaterals
Chapter 18 - Area of a Trapezium and a Polygon
Chapter 19 - Three-Dimensional Figures
Chapter 20 - Volume and Surface Area of Solids
Chapter 21 - Data Handling
Chapter 22 - Introduction to Coordinate Geometry
Chapter 23 - Line Graphs and Linear Graphs
Chapter 24 - Pie Charts
Chapter 25 - Probability
The 9th class marks the beginning of high school, and the concepts that will be taught here will be constantly recalled to explain the concepts in higher classes. To help students make mathematics their strength, the Aakash Institute provides solutions to RS Aggarwal. Chapter 1 explains the concept of Number Systems, which include rational and irrational numbers, real numbers representing the numbers on a number line, rationalisation and laws of exponents. Chapter 2 has problems based on various topics like algebraic expressions, Polynomials of various degrees, number of terms in a polynomial, value of a polynomial, zeros of a polynomial, division algorithm and factor theorem.
Chapter 3 contains problems based on methods of factorisation, factorisation of the difference of two squares, quadratic trinomials, the square of a trinomial, cube of a binomial and factorisation of sum or difference of cubes. Linear Equations in Two Variables and the Graph of a Linear Equation in Two Variables are discussed in chapter 4. Chapter 5 covers some concepts like cartesian coordinates, coordinate system and methods used to plot a graph. Axioms and Postulates, Euclid's five postulates, and determining the number of lines passing between two given points is covered in Chapter 6. The seventh chapter teaches pupils the several types of angles, relationships, and results on parallel lines. Chapter 8 has topics like types of Triangles based on sides and angles and exterior and interior angles. Geometry is one of the important topics in Class 9 as it will be continued in higher grades.
Congruence connection in the set of all Triangles and Inequalities in a Triangle are two concepts covered in the ninth chapter. Chapter 10 tells us about the various quadrilaterals, including parallelograms, rectangles, rhombuses and square and midpoint theorem. Topics covered in Chapter 11 include Euclidean area axioms, figures with the same base and parallels, Parallelograms, and numerous theorems. In the 12th chapter, the principles based on circles are taught. This chapter covers essential subjects such as circle words, arcs of a circle, congruence, angles subtended by arcs, and quadrilateral outcomes. Chapter 13 has problems based on constructing figures like the perpendicular bisector of a line segment and drawing the perpendicular bisector of a given line segment and triangles. Chapter 14 has 1 exercise based on concepts like important formulas and methods used to find areas of Triangles and Quadrilaterals.
The 15th chapter covers formulae and methods for calculating the volume and surface area of cuboids, cubes, cylinders, right circular cones, spheres, spherical shells, and hemispheres. The sixteenth chapter shows how to display data in a tabular manner and employ crucial formulae to solve issues. The principles of graphical representation of data, bar graph, histogram, and the process of generating a Frequency Polygon are covered in Chapter 17. Chapter 18 contains problems and formulas used to find the mean, median, and mode of ungrouped data. Probability is a crucial chapter in Class 9 since some of the concepts are applied in higher education. The words related to probability and operations are covered in detail in this chapter.
Chapter 1 - Number System
Chapter 2 - Polynomials
Chapter 3 - Factorisation of Polynomials
Chapter 4 - Linear Equations in Two Variables
Chapter 5 - Coordinate Geometry
Chapter 6 - Introduction to Euclid's Geometry
Chapter 7 - Lines and Angles
Chapter 8 - Triangles
Chapter 9 - Congruence of Triangles and Inequalities in a Triangle
Chapter 10 - Quadrilaterals
Chapter 11 - Areas of Parallelograms and Triangles
Chapter 12 - Circles
Chapter 13 - Geometrical Constructions
Chapter 14 - Areas of Triangles and Quadrilaterals
Chapter 15 - Volumes and Surface Area of Solids
Chapter 16 - Presentation of Data in Tabular Form
Chapter 17 - Bar Graph, Histogram and Frequency Polygon
Chapter 18 - Mean, Median and Mode of Ungrouped Data
Chapter 19 - Probability
We continue exploring real numbers in Chapter 1 of the RS Aggarwal Textbook, beginning with Euclid's Division Lemma and The Fundamental Theorem of Arithmetic. Chapter 2 deals with polynomials and their related concepts, including the value of a polynomial at a point, Zeros of a polynomial, and its general form. A polynomial is said to be linear, quadratic, or even a higher degree. In Chapter 3, the concepts discussed are Solution of a Linear Equation, Simultaneous Linear Equations In Two Variables, Solution of a Given System of Two Simultaneous Equations, Consistent and Inconsistent Systems of Linear Equations. Methods of solving the Simultaneous Linear Equations include the graphical method, the algebraic method covering the substitution or elimination methods, etc.
Quadratic Equations is the subject of Chapter 4. The first people to solve quadratic equations of the type x2 – px + q=0 were the Babylonians. An Indian mathematician named Brahmagupta (AD 598–665) devised an explicit solution for solving a quadratic equation of the type ax2–bx=c. Chapter 5 deals with Arithmetic Progression with Arithmetic Series, finding the general term of an AP, Arithmetic Mean, Sum of n terms of an AP. Chapter 6 discusses Coordinate Geometry, graphs of linear equations, the distance between two points, section formula and area of the triangle, etc. Chapter 7 deals with Triangles, congruent figures and similar figures, Similar Polygons, Equiangular Triangles, and Similar Triangles, Thales Theorem, Converse of Thales Theorem, Midpoint Theorem, Angle-Bisector Theorem, AAA-similarity, SSS-similarity, SAS- similarity, Pythagoras Theorem and more.
Chapter 8 deals with Circles, secant, tangent, number of tangents to a circle, length of a tangent. Chapter 9 discusses the topic of Constructions. Students learn about dividing a line segment in a given ratio, tangent to a circle from a point outside it, and constructing a triangle similar to a given triangle. Chapter 10 deals with the topic of Trigonometric Ratios, Trigonometric Ratios(T-Ratios) of An Acute Angle of a Right Triangle, Reciprocal Relation, T-Ratios of Angles Are Well-Defined, Quotient Relation of T-Ratios, Square Relation etc. Chapter 11 talks about T-Ratios of Some Particular Angles that are 45°, 60° and 30°as well as Axioms For T-Ratios of 0° and Axioms For T-Ratios of 90° are also discussed. In chapter 12, the topic discussed in detail is the Trigonometric Ratios of Complementary Angles. Chapter 13 discusses some of the trigonometric identities. Finally, the topic of heights and distances and problems related to heights and distances is the focus of Chapter 14.
Chapter 15 deals with Perimeter and Area of Plane Figures. Chapter 16 deals with the topic of "Area of Circle, Sector and Segment". The concepts discussed include the area of a circle, area of sectors and segments of a circle, problems based on areas and perimeter/ circumference of the given plane figures etc. Chapter 17 constitutes topics related to Volume and Surface Areas of Solids. The concepts covered are surface areas and volumes of cubes, cuboids, spheres, hemispheres and right circular cylinders/ cones, frustum of a cone etc. Chapter 18 deals with three measures of central tendency, namely (a) mean, (b) median and (c) mode. Chapter 19 deals with simple probability and problems on single events.
Chapter 1 - Real Numbers
Chapter 2 - Polynomials
Chapter 3 - Linear equations in two variables
Chapter 4 - Triangles
Chapter 5 - Trigonometric Ratios
Chapter 6 - T-Ratios of Some Particular Angles
Chapter 7 - Trigonometric Ratios of Complementary Angles
Chapter 8 - Trigonometric Identities
Chapter 9 - Mean, Median, Mode of Grouped Data, Cumulative Frequency Graph and Ogive
Chapter 10 - Quadratic Equations
Chapter 11 - Arithmetic Progressions
Chapter 12 - Circles
Chapter 13 - Constructions
Chapter 14 - Height and Distance
Chapter 15 - Probability
Chapter 16 - Co-ordinate Geometry
Chapter 17 - Perimeter and Areas of Plane Figures
Chapter 18 - Areas of Circle, Sector and Segment
Chapter 19 - Volume and Surface Areas of Solids
The 11th grade marks the beginning of the college section, and the theorems, concepts and mathematical tools given to you from now onwards are used in real-world applications. These concepts are vital to the scientific scenario and the market that is viable today. These chapters are sophisticated and complex, which makes them difficult to understand and implement. This is where the Aakash RS Aggarwal Solutions help the students by providing the step-by-step solutions of each chapter. Chapter 1 discussed sets, properties of sets, types of sets, power set, universal set, union Venn diagram, union and intersection of sets, difference & complement of sets and properties of components.
Chapter 2 discusses the relations, and chapter 3 discusses functions. Important topics are ordered pair, the cartesian product of the sets, pictorial diagrams, domain, co-domain and range of a relation, pictorial representation of a function, domain, co-domain and range of a function, real-valued functions, domain and range of these functions, constant, identity, polynomial, rational, modulus, signum, exponential, logarithmic and greatest integer functions, with their graphs. Chapter 4 is the Principle of Mathematical Induction.
Important topics from this chapter are the process of the proof by induction, motivating the application of the method by looking at natural numbers. Chapter 5 discusses Complex Numbers and Quadratic Equations, the Need for complex numbers, especially √−1, algebraic properties of complex numbers, argand plane and polar representation of complex numbers. Algebraic solutions of linear inequalities in one variable and their representation on the number line, graphical solution of linear inequalities in two variables, graphical method of finding a solution of the system of linear inequalities in two variables are discussed in chapter 6 & 7. The fundamental principle of counting, factorial, permutations and combinations, derivation of formulae form of nPr and nCr and their connections, simple applications are discussed in chapter 8 & 9 under Permutation and Combination.
Chapter 10 is about the Binomial Theorem. The chapter contains the theory (statement and proof) of the binomial theorem for positive integral indices, knowledge of Pascal's triangle, general and middle term in binomial expansion, and simple applications include a few important topics. Chapter 11, 12 and 13 are related to Series and Sequence, namely arithmetic progression, geometrical progression and some special series. Chapter 14 to 19 are about trigonometric functions and angles. Few important topics of these chapters are positive and negative angles, measuring angles in radians and in degrees, the definition of trigonometric functions with the help of unit circle, signs of trigonometric functions, domain and range of trigonometric functions, their graphs and their simple applications.
From chapter 20 to 26, the textbook discusses coordinate geometry. Few important topics of coordinate geometry are Shifting of origin, the slope of a line and angle between two lines, various forms of equations of a line: parallel to the axis, point-slope form, slope-intercept form, two-point form, intercept form and normal form, a distance of a point from a line, standard equations and simple conic sections like parabola, ellipse and hyperbola, standard equation of a circle, Coordinate axes and coordinate planes in three dimensions and distance between two points and section formula.
Chapter 27 and 28 are about calculus. Important topics among them are derivative, limits of polynomials and rational functions, trigonometric, exponential and logarithmic functions. The definition of derivative relates to the slope of the curve's tangent, a derivative of the sum, difference, product and quotient of functions and derivatives of polynomial or trigonometric functions. Chapter 29 is about mathematical reasoning; it involves validating the statements involving the connecting words. Measures of Dispersion: Range, Mean deviation, variance and standard deviation of ungrouped/grouped data and analysis of frequency distributions with equal means but different variances are studied in chapter 30. Chapter 31 is about probability, random experiments, outcomes, sample spaces, the occurrence of events, 'not', 'and' and 'or' events, exhaustive events, mutually exclusive events etc.
Chapter 1 Sets
Chapter 2 Relations
Chapter 3 Functions
Chapter 4 Principle Of Mathematical Induction
Chapter 5 Complex Numbers And Quadratic Equations
Chapter 6 Linear Inequations (In One Variable)
Chapter 8 Permutations
Chapter 9 Combinations
Chapter 10 Binomial Theorem
Chapter 11 Arithmetic Progression
Chapter 12 Geometrical Progression
Chapter 13 Some Special Series
Chapter 14 Measurement Of Angles
Chapter 15 Trigonometric, Or Circular, Functions
Chapter 16 Conditional Identities Involving The Angles Of A Triangle
Chapter 17 Trigonometric Equations
Chapter 18 Solution Of Triangles
Chapter 19 Graphs Of Trigonometric
Chapter 20 Straight Lines
Chapter 21 Circle
Chapter 22 Parabola
Chapter 23 Ellipse
Chapter 24 Hyperbola
Chapter 25 Applications Of Conic Sections
Chapter 26 Three-Dimensional Geometry
Chapter 27 Limits
Chapter 28 Differentiation
Chapter 29 Mathematical Reasoning
Chapter 30 Statistics
Chapter 31 Probability
The 12th grade is built upon the concepts of class 11th. Various new concepts are given here, and they are equally crucial to engineering and economic mathematics. To help with the maths proficiency of the students, the Aakash institute prepares the solutions explaining these concepts. Chapter 1 will study relation in a set, domain, and range in relation. In chapter 2, we will learn about the domain and co-domain of functions and invertible functions. In chapter 3 of binary operations, we will learn the concept of binary operation and new operations. Chapter 4 deals with inverse trigonometry. Chapter 5 teaches about matrix, matrix operations, matrix multiplication, transposing of matrix, symmetry and skew-symmetric matrix, and inverse matrix. Chapter 6 will learn that a determinant is the arrangement of numbers in rows and columns where each determinant has a fixed value. Chapter 7 deals with the invertible matrix and some results of the invertible matrix.
Chapter 8 will learn about the method of solving a system of linear equations using the matrix method. Chapter 9 explains real functions, important functions, graphs, graphs on trigonometric functions, continuity and differentiability. Chapter 10 will understand derivatives of a function, inverse trigonometric functions, and differentiation by trigonometric transformations. Applications of Derivatives, Derivative as a rate measure, errors and approximation, Rolle's and Lagrange's theorem, etc., are the important topics covered in chapter 11. Chapter 12 mainly deals with partial fractions, integration using partial fractions. The fundamental theorem of integral calculus, evaluating a definite integral by substitution, etc., are the concepts explained in chapter 13.
The concepts like special integrals and theorems based on them are explained in chapter 14. Chapter 15 mainly deals with partial fractions, integration using partial fractions. Chapter 16 explains the methods of evaluating definite integrals in a stepwise manner. Determining the areas of various bounded regions are explained in chapter 17. Chapter 18 has problems on the differential equation, solution and general solution of a differential equation and a differential equation's formation whose general solution is given. Chapter 19 involves solving differential equations.
In Chapter 20, problems are based on proving that the given set of differential equations are homogeneous. Chapter 21 has problems with linear differential equations. Chapter 22 deals with vectors, the law of addition vectors, scalar multiplication of a vector and section formulae. Chapter 23 covers topics like the angle between two vectors, projection, properties of the scalar product. Chapter 24 deals with vector products of two vectors, properties of vector products, the law of parallelogram, etc. Theorems on the scalar triple product are explained in chapter 25. Chapter 26 covers coordinates of a point in space, some results on points in space and some results on lines in space.
Chapter 27 teaches about the equation of the line in various conditions in vector and Cartesian form. Chapter 28 provides knowledge about the general equation of a plane in Cartesian and vector form. Chapter 29 deals with problems on conditional probability and the probability of independent events. The theorem of total probability, known as Bayes's theorem and its applications, are covered in chapter 30. Chapter 31 provides basic knowledge of the probability distribution of a random variable and the mean and variance of a random variable. In chapter 32, students learn about Bernoulli's Theorem, conditions for applicability and mean and variance of a binomial distribution. The steps to be followed in constructing the graph of linear inequation and linear programming are covered in chapter 33.
Chapter 1 Relations
Chapter 2 Functions
Chapter 3 Binary Operations
Chapter 4 Inverse Trigonometric Functions
Chapter 5 Matrices
Chapter 6 Determinants
Chapter 7 Adjoint & Inverse Of A Matrix
Chapter 8 System Of Linear Equations
Chapter 9 Continuity & Differentiability
Chapter 10 Differentiation
Chapter 11 Application Of Derivative
Chapter 12 Indefinite Integration
Chapter 13 Method Of Integration
Chapter 14 Some Special Integrals
Chapter 15 Integration Using Partial Fractions
Chapter 16 Definite Integrals
Chapter 17 Area Of Bounded Regions
Chapter 18 Differential Equation & Their Formation
Chapter 19 Differential Equations With Variable Separable
Chapter 20 Homogeneous Differential Equations
Chapter 21 Linear Differential Equation
Chapter 22 Vector And Their Properties
Chapter 23 Scalar Or Dot Product Of Vectors
Chapter 24 Cross Or Vector Product Of Vectors
Chapter 25 Product Of Three Vectors
Chapter 26 Fundamental Concept Of 3-Dimensional Geometry
Chapter 27 Straight Line In A Space
Chapter 28 The Plane
Chapter 29 Probability
Chapter 30 Bayes Theorem & Its Applications
Chapter 31 Probability Distribution
Chapter 32 Binomial Distribution
Chapter 33 Linear Programming
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